Finite Group DatabasebetaFinite Group DatabasebetaOrder 35072.
502 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 502 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C137 | #392 |
| commutator, Frattini, cosocle | C2×C42 | C23×C137 |
| prime radical | #3214×C137 | C2 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C137 ◁ C2×C42×C137 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #3254×C137 | C2 | semidirect |
| 2. #3235×C137 | C2 | semidirect |
| 4. #1963×C137 | C2 | semidirect |
| 5. #1506×C137 | C2 | semidirect |
| 6. #1505×C137 | C2 | semidirect |
| 7. #1307×C137 | C2 | semidirect |
| 202. #10214 | C137 | direct (N × H) |
| 203. C137 | #10214 | direct (N × H) |
| 204. #3254 | C2×C137 | semidirect |
| 205. #3235 | C2×C137 | semidirect |
| 207. #1963 | C2×C137 | semidirect |
| 208. #1506 | C2×C137 | semidirect |
| 209. #1505 | C2×C137 | semidirect |
| 210. #1307 | C2×C137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3254×C137 | 2 |
| #3235×C137 | 2 |
| #3214×C137 | 2 |
| #1963×C137 | 2 |
| #1506×C137 | 2 |
| #1505×C137 | 2 |
| #1307×C137 | 2 |
| #10214 | 137 |